class: center, middle, inverse, title-slide # M-FIT Trial ## Statistical Aspects ### 12 July 2021 --- # Primary Outcome - FACIT-Fatigue: - 13 item Likert scale, each Likert item scored from 0 to 4 `\(\to\)` total score from 0 to 52 - comparison between intervention groups at 12-weeks post-randomisation -- - visit schedule:  - longitudinal model for primary analysis --- background-image: url("data:image/png;base64,#facit-fatigue-scale.png") # FACIT-Fatigue Tool --- # Modelling Longitudinal model to include repeat measurement occasions. - `\(\texttt{treat}\)` - a treatment group (0: control, 1: walking, 2: resistance, 3: resistance + aerobic) - `\(\texttt{visit}\)` - a FACIT-Fatigue measurement occasion (baseline, 4 weeks, 8 weeks, 12 weeks) - `\(\mu_{\texttt{treat}, \texttt{visit}}\)` - mean FACIT-Fatigue at specific visit under specific treatment -- Marginally, for a subject `\(i\)`, unstructured mean: `$$\begin{aligned}Y_i &\sim \text{MVN}(\mu_{\texttt{treat}(i)},\Sigma)\\ \mu_{\texttt{treat},\texttt{visit}}&=\alpha+(\beta_{\texttt{visit}}+\xi_{\texttt{treat},\texttt{visit}})\times 1_{\texttt{visit}\ne\text{baseline}}\\ \alpha &\sim N(40, 5^2) \\ \beta_{\texttt{visit}} &\sim N(0, 5^2),\quad\texttt{visit}=4,8,12\\ \xi_{\texttt{treat},\texttt{visit}}&\sim N(0, 5^2),\quad\texttt{treat}=1,2,3,\ \texttt{visit}=4,8,12\end{aligned}$$` --- # Modelling (cont.) - interim analyses after 100, 200, 300 participants reach primary endpoint, final at 400 - update primary model and assess quantities of interest: - probability each active treatment better than all others, "**Pr(best)**" `$$\text{Pr}\left[\xi_{\texttt{treat},\text{12 weeks}}-\max_{\texttt{treat}^\star\ne\texttt{treat}}\xi_{\texttt{treat}^\star,12 \text{weeks}}>0\right],\quad\texttt{treat}=1,2,3$$` - probability each active treatment better than control, "**Pr(eff)**" `$$\text{Pr}\left[\xi_{\texttt{treat},12\text{ weeks}}>0\right],\quad\texttt{treat}=1,2,3$$` - update target allocations for active treatments, "**Pr(allocate)**": up-weight according to **Pr(best)** `$$\text{Pr}(\texttt{treat}_i=k)\propto \text{Pr}(\text{best}=k)^{c}$$` --- # Example - Interim 1, n = 100  --- # Example - Interim 2, n = 200  --- # Example - Interim 3, n = 300  --- # Example - Final, n = 400